The owners of Hellman’s mayonnaise have dropped a lawsuit claiming another company should stop selling a product under the name Just Mayo because it does not contain eggs.

The Unilever company originally filed suit against Hampton Creek, a small California company, on the basis that the name Just Mayo amounted to false advertising because being egg-free meant it could not be defined as mayonnaise.

It argued that the word “mayo” implied that the product was mayonnaise, and that Hampton Creek had stolen market share from Hellman’s.

Hampton Creek said it marketed its product as “mayo” rather than mayonnaise specifically to meet labelling regulations.

Unilever said on Thursday that it had decided to withdraw the lawsuit so that Hampton Creek could address its labelling directly with industry groups and regulatory authorities.

Hampton Creek’s chief executive, Josh Tetrick, said there had been positive conversations with industry groups and government officials. He said the company may make the word “just” larger on the label but had no plans to change the product’s name.

Just Mayo’s label states that it does not contain eggs. The label features a white egg with a plant growing in front, which Tetrick said was the company’s way of showing they used plants instead.

Unilever holds the biggest share of the US mayonnaise market, estimated to be worth $2bn (£1.28bn) annually, according to the market research firm Euromonitor.

Not all of its products, however, are exactly mayonnaise either. Shortly after filing the lawsuit, it tweaked references on its websites to products to refer to them as “mayonnaise dressing” rather than mayonnaise.

Tetrick said the lawsuit had been a boon to Hampton Creek, boosting sales of Just Mayo and giving the company “the opportunity to tell our story to millions of people”.

He commended Unilever for dropping the lawsuit, saying the company was “a classy bunch of people who realised that this isn’t aligned with their corporate ethos”.